Stochastic slowdown in evolutionary processes

Abstract

We examine birth--death processes with state dependent transition probabilities and at least one absorbing boundary. In evolution, this describes selection acting on two different types in a finite population where reproductive events occur successively. If the two types have equal fitness the system performs a random walk. If one type has a fitness advantage it is favored by selection, which introduces a bias (asymmetry) in the transition probabilities. How long does it take until advantageous mutants have invaded and taken over? Surprisingly, we find that the average time of such a process can increase, even if the mutant type always has a fitness advantage. We discuss this finding for the Moran process and develop a simplified model which allows a more intuitive understanding. We show that this effect can occur for weak but non--vanishing bias (selection) in the state dependent transition rates and infer the scaling with system size. We also address the Wright-Fisher model commonly used in population genetics, which shows that this stochastic slowdown is not restricted to birth-death processes.

8 pages, 3 figures, accepted for publication

References in corpus (13)

• Evolutionary games on graphs
• Brownian motors: noisy transport far from equilibrium
• Evolutionary game theory: Temporal and spatial effects beyond replicator dynamics
• Phase transitions and volunteering in spatial public goods games
• Coevolutionary Dynamics: From Finite to Infinite Populations
• Fixation of strategies for an evolutionary game in finite populations
• Cyclic dominance and biodiversity in well-mixed populations
• Stochasticity and evolutionary stability
• Fixation times in evolutionary games under weak selection
• Zero-one survival behavior of cyclically competing species
• Stochastic and Boltzmann-like models for behavioral changes, and their relation to game theory
• The edge of neutral evolution in social dilemmas
• Discrete versus continuous models in evolutionary dynamics: from simple to simpler -- and even simpler -- models

Cited by in corpus (11)

• Universality of weak selection
• Fixation in finite populations evolving in fluctuating environments
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• Evolutionary games on cycles with strong selection
• Finite-population evolution with rare mutations in asymmetric games
• Evolutionary dynamics in finite populations with zealots
• Environmental Evolutionary Graph Theory
• Random and non-random mating populations: Evolutionary dynamics in meiotic drive
• Fixation times on directed graphs
• q-deformed evolutionary dynamics in simple matrix games
• Fixation probabilities and hitting times under low levels of frequency-dependent selection